Solve k^2=1000left(150*250-50*550right)^2/200*800*300*700

$${ k }^{ 2 } = \frac{ 1000 { \left(150 \cdot 250-50 \cdot 550 \right) }^{ 2 } }{ 200 \cdot 800 \cdot 300 \times 700 }$$

Solve for k

$$k = \frac{5 \sqrt{210}}{42} \approx 1.725163898$$

$$k = -\frac{5 \sqrt{210}}{42} \approx -1.725163898$$

Steps by Finding Square Root

Cancel out 5\times 200 in both numerator and denominator.

$$k^{2}=\frac{\left(150\times 250-50\times 550\right)^{2}}{160\times 300\times 700}$$

Multiply 150 and 250 to get 37500.

$$k^{2}=\frac{\left(37500-50\times 550\right)^{2}}{160\times 300\times 700}$$

Multiply 50 and 550 to get 27500.

$$k^{2}=\frac{\left(37500-27500\right)^{2}}{160\times 300\times 700}$$

Subtract 27500 from 37500 to get 10000.

$$k^{2}=\frac{10000^{2}}{160\times 300\times 700}$$

Calculate 10000 to the power of 2 and get 100000000.

$$k^{2}=\frac{100000000}{160\times 300\times 700}$$

Multiply 160 and 300 to get 48000.

$$k^{2}=\frac{100000000}{48000\times 700}$$

Multiply 48000 and 700 to get 33600000.

$$k^{2}=\frac{100000000}{33600000}$$

Reduce the fraction \frac{100000000}{33600000} to lowest terms by extracting and canceling out 800000.

$$k^{2}=\frac{125}{42}$$

Take the square root of both sides of the equation.

$$k=\frac{5\sqrt{210}}{42} k=-\frac{5\sqrt{210}}{42}$$

Steps Using the Quadratic Formula

Cancel out 5\times 200 in both numerator and denominator.

$$k^{2}=\frac{\left(150\times 250-50\times 550\right)^{2}}{160\times 300\times 700}$$

Multiply 150 and 250 to get 37500.

$$k^{2}=\frac{\left(37500-50\times 550\right)^{2}}{160\times 300\times 700}$$

Multiply 50 and 550 to get 27500.

$$k^{2}=\frac{\left(37500-27500\right)^{2}}{160\times 300\times 700}$$

Subtract 27500 from 37500 to get 10000.

$$k^{2}=\frac{10000^{2}}{160\times 300\times 700}$$

Calculate 10000 to the power of 2 and get 100000000.

$$k^{2}=\frac{100000000}{160\times 300\times 700}$$

Multiply 160 and 300 to get 48000.

$$k^{2}=\frac{100000000}{48000\times 700}$$

Multiply 48000 and 700 to get 33600000.

$$k^{2}=\frac{100000000}{33600000}$$

Reduce the fraction \frac{100000000}{33600000} to lowest terms by extracting and canceling out 800000.

$$k^{2}=\frac{125}{42}$$

Subtract \frac{125}{42} from both sides.

$$k^{2}-\frac{125}{42}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{125}{42} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-\frac{125}{42}\right)}}{2}$$

Square 0.

$$k=\frac{0±\sqrt{-4\left(-\frac{125}{42}\right)}}{2}$$

Multiply -4 times -\frac{125}{42}.

$$k=\frac{0±\sqrt{\frac{250}{21}}}{2}$$

Take the square root of \frac{250}{21}.

$$k=\frac{0±\frac{5\sqrt{210}}{21}}{2}$$

Now solve the equation k=\frac{0±\frac{5\sqrt{210}}{21}}{2} when ± is plus.

$$k=\frac{5\sqrt{210}}{42}$$

Now solve the equation k=\frac{0±\frac{5\sqrt{210}}{21}}{2} when ± is minus.

$$k=-\frac{5\sqrt{210}}{42}$$

The equation is now solved.

$$k=\frac{5\sqrt{210}}{42} k=-\frac{5\sqrt{210}}{42}$$